{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:DW4T7W7Y2EMY43BIX6TD2TN3BP","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"d521870a103f80c0408621b6185d3a141ea6e1bb72cd4e715dad42960dea5ca1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-02-25T14:12:01Z","title_canon_sha256":"7defce6807104f1bcd28212ed2b45e0f50897085e32ab7d7dff4198abab4da96"},"schema_version":"1.0","source":{"id":"1302.6097","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.6097","created_at":"2026-05-18T00:40:35Z"},{"alias_kind":"arxiv_version","alias_value":"1302.6097v1","created_at":"2026-05-18T00:40:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.6097","created_at":"2026-05-18T00:40:35Z"},{"alias_kind":"pith_short_12","alias_value":"DW4T7W7Y2EMY","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DW4T7W7Y2EMY43BI","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DW4T7W7Y","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:91c39019fe0a670f22e6e1e56b76f9f69c77deeccaf360b190b9998f2ad8dce6","target":"graph","created_at":"2026-05-18T00:40:35Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study polynomials with integer coefficients which become Eisenstein polynomials after the additive shift of a variable. We call such polynomials shifted Eisenstein polynomials. We determine an upper bound on the maximum shift that is needed given a shifted Eisenstein polynomial and also provide a lower bound on the density of shifted Eisenstein polynomials, which is strictly greater than the density of classical Eisenstein polynomials. We also show that the number of irreducible degree $n$ polynomials that are not shifted Eisenstein polynomials is infinite. We conclude with some numerical r","authors_text":"Igor E. Shparlinski, Randell Heyman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-02-25T14:12:01Z","title":"On Shifted Eisenstein Polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.6097","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:de467754faa01acdb03c4f42383e572868db914c65f98cbf6ec8cf772e162185","target":"record","created_at":"2026-05-18T00:40:35Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"d521870a103f80c0408621b6185d3a141ea6e1bb72cd4e715dad42960dea5ca1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-02-25T14:12:01Z","title_canon_sha256":"7defce6807104f1bcd28212ed2b45e0f50897085e32ab7d7dff4198abab4da96"},"schema_version":"1.0","source":{"id":"1302.6097","kind":"arxiv","version":1}},"canonical_sha256":"1db93fdbf8d1198e6c28bfa63d4dbb0bcbb7488bb20bdb7afbea666844115c41","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1db93fdbf8d1198e6c28bfa63d4dbb0bcbb7488bb20bdb7afbea666844115c41","first_computed_at":"2026-05-18T00:40:35.237271Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:35.237271Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FquG+OfrDt4lvXuuluzWqwk1iVTwf2+5denxVkhrG2vIidcfqSX118qsAZSIqMsx0oaK9PGHxY/rzMGxWnqCAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:35.237955Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.6097","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de467754faa01acdb03c4f42383e572868db914c65f98cbf6ec8cf772e162185","sha256:91c39019fe0a670f22e6e1e56b76f9f69c77deeccaf360b190b9998f2ad8dce6"],"state_sha256":"f9307ba04b691c87c07997abe2ddc97f50953ab4459a6a7517b866d1f0926206"}